MinT - Best Known (105−32, 105, s)-Nets in Base 16

Best Known (105−32, 105, s)-Nets in Base 16

(105−32, 105, 1036)-Net over F₁₆ — Constructive and digital

Digital (73, 105, 1036)-net over F₁₆, using

1 times m-reduction [i] based on digital (73, 106, 1036)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (20, 36, 518)-net over F₁₆, using
    - trace code for nets [i] based on digital (2, 18, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. digital (37, 70, 518)-net over F₁₆, using
    - trace code for nets [i] based on digital (2, 35, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(105−32, 105, 9933)-Net over F₁₆ — Digital

Digital (73, 105, 9933)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−32, 105, large)-Net in Base 16 — Upper bound on s

There is no (73, 105, large)-net in base 16, because

30 times m-reduction [i] would yield (73, 75, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]